Nikita Sharma 2019W2 MATH 101 209
Assignment Homework 10 due 9/12/14 at 9pm
Input C for convergence and D for divergence:
1. (1 point) Each of the following statements is an attempt
to show that a given series is convergent or divergent not using Note: You have only one chance to enter your answer.
the Comparison Test (NOT the Limit Comparison Test.) For Correct Answers:
each statement, enter C (for ”correct”) if the argument is valid, • C
or enter I (for ”incorrect”) if any part of the argument is flawed.
(Note: if the conclusion is true but the argument that led to it 3. (1 point)
was wrong, you must enter I.) Determine whether the following series converges or di-
verges.
∞
4n
1 1 1 ∑ 3 + 5n
1. For all n > 2, < 2 , and the series con- n=1
n2 − 3 n ∑ n2
1 Input C for convergence and D for divergence:
verges, so by the Comparison Test, the series ∑ 2
n −3
converges. Note: You have only one chance to enter your answer.
sin2 (n) 1 1 Correct Answers:
2. For all n > 1, < 2 , and the series ∑ 2 con-
n2 n n • C
sin2 (n)
verges, so by the Comparison Test, the series ∑ 4. (1 point)
n2
converges. Determine whether the following series converges or di-
n 2 1
3. For all n > 2, 3 < , and the series 2 ∑ 2 con- verges.
n − 3 n2 n ∞
n9 + 8
n
verges, so by the Comparison Test, the series ∑ 3 ∑ 10
n −3 n=1 n + 3
converges. √
n+1 1 1 Input C for convergence and D for divergence:
4. For all n > 2, > , and the series ∑ diverges,
n n n
√
n+1 Note: You have only one chance to enter your answer.
so by the Comparison Test, the series ∑ di- Correct Answers:
n
verges. • D
log(n) 1 1
5. For all n > 2, > 2 , and the series ∑ 2 con- 5. (1 point) Determine whether the following series con-
n2 n n
log(n) verges or diverges.
verges, so by the Comparison Test, the series ∑ ∞
n2 9
converges. ∑ n2n
arctan(n) π π 1 n=1
6. For all n > 1, < 3 , and the series ∑ 3
n3 2n 2 n Input C for convergence and D for divergence:
converges, so by the Comparison Test, the series
arctan(n)
∑ n3 converges. Note: You have only one chance to enter your answer.
Correct Answers:
Correct Answers:
• C
• I
• C 6. (1 point) Determine whether the following series con-
• C verges or diverges:
• C ∞
6
• I ∑ sin n
• C n=1
2. (1 point) Input C for convergence and D for divergence:
Determine whether the following series converges or di-
verges: Note: You have only one chance to enter your answer.
∞
Correct Answers:
n
∑ (n5 + 2)1/2 • D
n=1
1
Assignment Homework 10 due 9/12/14 at 9pm
Input C for convergence and D for divergence:
1. (1 point) Each of the following statements is an attempt
to show that a given series is convergent or divergent not using Note: You have only one chance to enter your answer.
the Comparison Test (NOT the Limit Comparison Test.) For Correct Answers:
each statement, enter C (for ”correct”) if the argument is valid, • C
or enter I (for ”incorrect”) if any part of the argument is flawed.
(Note: if the conclusion is true but the argument that led to it 3. (1 point)
was wrong, you must enter I.) Determine whether the following series converges or di-
verges.
∞
4n
1 1 1 ∑ 3 + 5n
1. For all n > 2, < 2 , and the series con- n=1
n2 − 3 n ∑ n2
1 Input C for convergence and D for divergence:
verges, so by the Comparison Test, the series ∑ 2
n −3
converges. Note: You have only one chance to enter your answer.
sin2 (n) 1 1 Correct Answers:
2. For all n > 1, < 2 , and the series ∑ 2 con-
n2 n n • C
sin2 (n)
verges, so by the Comparison Test, the series ∑ 4. (1 point)
n2
converges. Determine whether the following series converges or di-
n 2 1
3. For all n > 2, 3 < , and the series 2 ∑ 2 con- verges.
n − 3 n2 n ∞
n9 + 8
n
verges, so by the Comparison Test, the series ∑ 3 ∑ 10
n −3 n=1 n + 3
converges. √
n+1 1 1 Input C for convergence and D for divergence:
4. For all n > 2, > , and the series ∑ diverges,
n n n
√
n+1 Note: You have only one chance to enter your answer.
so by the Comparison Test, the series ∑ di- Correct Answers:
n
verges. • D
log(n) 1 1
5. For all n > 2, > 2 , and the series ∑ 2 con- 5. (1 point) Determine whether the following series con-
n2 n n
log(n) verges or diverges.
verges, so by the Comparison Test, the series ∑ ∞
n2 9
converges. ∑ n2n
arctan(n) π π 1 n=1
6. For all n > 1, < 3 , and the series ∑ 3
n3 2n 2 n Input C for convergence and D for divergence:
converges, so by the Comparison Test, the series
arctan(n)
∑ n3 converges. Note: You have only one chance to enter your answer.
Correct Answers:
Correct Answers:
• C
• I
• C 6. (1 point) Determine whether the following series con-
• C verges or diverges:
• C ∞
6
• I ∑ sin n
• C n=1
2. (1 point) Input C for convergence and D for divergence:
Determine whether the following series converges or di-
verges: Note: You have only one chance to enter your answer.
∞
Correct Answers:
n
∑ (n5 + 2)1/2 • D
n=1
1
